Question

class 9 -an isosceles right triangle has area 8cm² . then length of its hypotenuse is​

Answer 1

Given, area of an isosceles right triangle = 8 cm2

Area of an isosceles triangle = 1/2 (Base x Height)

⇒ 8 = 1/2 (Base x Base)

[∴ base = height, as triangle is an isosceles triangle]

⇒ (Base)2 =16 ⇒ Base= 4 cm

In ΔABC, using Pythagoras theorem

AC2 = AB2 + BC2 = 42 + 42 = 16 + 16

⇒ AC2 = 32 ⇒ AC = √32 cm

[taking positive square root because length is always positive]

Hence, the length of its hypotenuse is √32 cm.

hope that helps:)

Answer 2

$ANSWER$

Given, area of an isosceles right triangle = 8 cm²

Area of an isosceles triangle = 1/2 (Base x Height)

⇒ 8 = 1/2 (Base x Base)

[∴ base = height, as triangle is an isosceles triangle]

⇒ (Base)2 =16 ⇒ Base= 4 cm

In ΔABC, using Pythagoras theorem

AC² = AB² + BC² = 42 + 42 = 16 + 16

⇒ AC² = 32 ⇒ AC = √32 cm

[taking positive square root because length is always positive]

Hence, the length of its hypotenuse is √32 cm.

hope it helpful to you.

thank you.